Approximate Inference Control (AICO) is a method for solving Stochastic Optimal Control (SOC) problems. The general idea is to think of control as the problem of computing a posterior over trajectories and control signals conditioned on constraints and goals. Since exact inference is infeasible in realistic scenarios, the key for high-speed planning and control algorithms is the choice of approximations. In this talk I will introduce to the general approach, discuss its intimate relations to DDP and the current research on Kalman's duality, and discuss the approximations that we use to get towards real-time planning in high-dimensional robotic systems. I will also mention recent work on using Expectation Propagation and truncated Gaussians for inference under hard constraints and limits as they typically arise in robotics (collision and joint limit constraints).